The free vibration of rotating bending-torsional composite Timoshenko beams (CTBs) with arbitrary boundary conditions is analyzed. The composite material coupled rigidity, Coriolis effects and the separation of the cross-section’s mass and shear centers are considered and they will cause the bending-torsion coupled vibration of the beam. Based on the Hamilton’s principle, the governing partial differential matrix equation of motion of the beam are formulated with variable coefficients. Those equations containing variable coefficients are expressed in a special matrix form in terms of the flexural translation, rotation of cross section and torsional rotation of the beam. The differential transform matrix method (DTMM), which is an improved approach from the traditional differential transform method (DTM), is proposed to deal with the governing matrix equation with corresponding boundary conditions. The mode shapes and natural frequencies of the beam are obtained. Cantilevers are calculated as examples to verify the present theory and investigate the dynamic characteristics of the rotating CTB. The present results are consistent with those reported in the literature and those calculated from COMSOL. The influence of the composite material rigidity, rotation speed, hub radius and axial load on the natural frequencies and mode shapes of the beam are studied, while the frequency veering and mode shift phenomena are observed. Furthermore, the beam’s critical buckling loads corresponding to the axial load are found.

分析了任意边界条件下的旋转弯曲扭转复合Timoshenko梁（CTBs）的自由振动。考虑了复合材料的耦合刚度，科里奥利效应以及横截面的质心和剪切中心的分离，它们将导致梁的弯扭耦合振动。根据汉密尔顿原理，用可变系数来表达控制梁运动的偏微分矩阵方程。这些包含可变系数的方程式以挠曲平移，横截面旋转和梁的扭转旋转以特殊的矩阵形式表示。差分变换矩阵方法（DTMM），它是对传统差分变换方法（DTM）的改进，提出了处理具有相应边界条件的控制矩阵方程的方法。获得了光束的模态形状和固有频率。以悬臂为例，验证了本理论并研究了旋转CTB的动态特性。目前的结果与文献报道和COMSOL计算得出的结果一致。研究了复合材料的刚度，转速，轮毂半径和轴向载荷对梁的固有频率和振型的影响，同时观察了频率转向和振型现象。此外，找到了与轴向载荷相对应的梁的临界屈曲载荷。以悬臂为例，验证了本理论并研究了旋转CTB的动态特性。目前的结果与文献报道和COMSOL计算得出的结果一致。研究了复合材料的刚度，转速，轮毂半径和轴向载荷对梁的固有频率和振型的影响，同时观察了频率转向和振型现象。此外，找到了与轴向载荷相对应的梁的临界屈曲载荷。以悬臂为例，验证了本理论并研究了旋转CTB的动态特性。目前的结果与文献报道和COMSOL计算得出的结果一致。研究了复合材料的刚度，转速，轮毂半径和轴向载荷对梁的固有频率和振型的影响，同时观察了频率转向和振型现象。此外，找到了与轴向载荷相对应的梁的临界屈曲载荷。研究了轮毂半径和轴向载荷对梁固有频率和振型的影响，同时观察了频率转向和振型变化现象。此外，找到了与轴向载荷相对应的梁的临界屈曲载荷。研究了轮毂半径和轴向载荷对梁固有频率和振型的影响，同时观察了频率转向和振型变化现象。此外，找到了与轴向载荷相对应的梁的临界屈曲载荷。